, Volume 163, Issue 1, pp 1-24
Date: 19 Oct 2005

Correlations for pairs of closed geodesics

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In this article we consider natural counting problems for closed geodesics on negatively curved surfaces. We present asymptotic estimates for pairs of closed geodesics, the differences of whose lengths lie in a prescribed family of shrinking intervals. Related pair correlation problems have been studied in both Quantum Chaos and number theory.